{"paper":{"title":"On the Azuma inequality in spaces of subgaussian of rank $p$ random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Zajkowski","submitted_at":"2017-01-11T18:58:44Z","abstract_excerpt":"For $p > 1$ let a function $\\varphi_p(x) = x^2/2$ if $|x|\\le 1$ and $\\varphi_p(x) = 1/p|x|^p -1/p + 1/2$ if $|x| > 1$. For a random variable $\\xi$ let $\\tau_{\\varphi_p}(\\xi)$ denote $\\inf\\{c\\ge 0 :\\; \\forall_{\\lambda\\in\\mathbb{R}}\\; \\ln\\mathbb{E}\\exp(\\lambda\\xi)\\le\\varphi_p(c\\lambda)\\}$; $\\tau_{\\varphi_p}$ is a norm in a space $Sub_{\\varphi_p}(\\Omega) =\\{\\xi:\n  \\; \\tau_{\\varphi_p}(\\xi) <\\infty\\}$ of $\\varphi_p$-subgaussian random variables which we call {\\it subgaussian of rank $p$ random variables}. For $p = 2$ we have the classic subgaussian random variables. The Azuma inequality gives an es"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03099","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}